What is the definition of a dollar now without gold backing? It seems that a dollar is now just an entry in a book somewhere in some bank. Or it is the federal reserve note? Or is it both? I understand the concept of the monetary base. But what I don't understand is how this works. If a dollar is in part just an entry in a book, what stops some bank from simply claiming they have an infinite amount of dollars? Or is there some central registry that claims to keep track of how many dollars each bank has? (This would seem absurd to me. How then would foreign banks holding US dollars keep track of how many dollars they had?) If there is no central registry, then how do you prevent people claiming to have dollars on their books?

I think explaining what a dollar is would go toward answering these questions.

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A dollar is money which can be used in the United States to purchase goods and services and to repay debts. It can sometimes be used for these purposes in some other parts of the world.

If a bank says it has an unlimited amount of dollars, then it will presumably be willing to lend them to customers, who will then want to spend them.

The bank will then either have to give the customer dollar bills (Federal Reserve Notes which presumably it does not have in unlimited amounts) or be willing to transfer dollars to another bank on the instruction of its customer.

The other bank may then expect this to be settled. Unless there are also flows into the first bank to offset the amount owed, it can only settle with dollar bills (but faces the same issue as before) or by instructing a third bank where it has an account to transfer dollars to the second bank. This can continue up the chain until an instruction to transfer funds reaches the U.S. Federal Reserve Banks, where the top commercial banks hold their reserve deposits.

Other banks will not be impressed with the first bank simply saying it has unlimited dollars if it does not have accounts with other banks with dollars to support the transfers. Writing numbers in your own books does not change the numbers in other banks' books. The constraints that this causes is one of the constraints on lending and so on the creation of money.

A dollar is a medium of exchange produced by the federal reserve at the federal government's behest. Like all fiat currency it has no intrinsic value, but is worth something because people agree it is. This is nothing unusual...currencies with little or no intrinsic value are historically common.

Banks keep track of how many dollars people have given them (whether savers or investors) and what they have paid out, so they always know what their balance is and don't lend money they don't have. The thing that prevents them from claiming infinite money is the same thing that keeps me from claiming I have a million dollars under my mattress: it's fraud. If a bank was to lie about its balances, the bank's auditors and regulators would be happy to start throwing those responsible in jail and correcting the mistake.

There is exactly one bank that can just change its balances or pay with dollars that it didn't acquire from others: the federal reserve. When the fed wants to buy something it doesn't have to worry about where the dollars come from: it just makes the dollars up electronically. This is why the fed can never go bankrupt. It doesn't have meaningful liabilities.

Now, fractional banking increases the number of apparent dollars in the aggregate economy because any time someone deposits in a bank, the dollar is then lent out. Both the borrower and lender would say they have a dollar. But of course, this process results in a more-or-less constant multiplier of the apparent dollars, so it's not what causes inflation, nor is it anything strange or evil.

I'm probably going to kick a hornet's nest by saying this, but I suspect that modern USD value is rooted in the fact that the US Treasury must remit USD to bond holders (particularly the Fed) at maturity. All other sources of USD value are likely subsidiary to that demand.

US taxes must be paid in USD; that demand provides value in the broader economy, but I suspect that is secondary to and stems from Treasury's need to pay off bonds in USD.

As a tertiary effect, US taxes provide taxpayers access to services, infrastructure, and certain goods; it could be said that USD's value stems in part from those things. For instance, US taxes help support the quality of US schools, roads, libraries, military, and police. This effect is diluted, though, by the fact that there are social contract and governance issues that emerge when you get to this layer.

Fourth-order sources of value would include global valuations of USD as a reserve and international payment currency. In other words, the currency is traded globally because US taxpayers feel like they get something in return when they pay their US taxes.

If all of the above is true, then it would follow that reducing tax revenues or shrinking government should reduce currency demand at home, leading to inflation, and vice versa. We see some of these effects in various experiments throughout history, not only in the US but elsewhere.

The U.S. dollar (as opposed to the Canadian Australian dollars) is a unit of account: a way to measure the value of monetary instruments. For example a \$20 bill is an instrument with a value of 20 units, with the unit being a dollar. Debts are measured in this unit, and there are laws that regulate how such debts are discharged via the transfer of instruments.

These monetary instruments can be organised into various measures of money supply (monetary base, M1, etc.). Which instruments you want to consider to be “money” probably depends on what you want to analyse.

The monetary base (mainly) consists of two types of instruments: notes and coins (“currency in circulation”) issued by entities with the Federal government, and deposits at the Federal Reserve (“bank reserves”). Although the private sector can settle transactions using other means (debit and credit cards, cheques (checks in American English)), ultimately these government-issued instruments will back up the private instruments, since banks settle between themselves via transferring balances at the Federal Reserve.

The fact that the private sector layers its own instruments on top of government-issued instruments explains why the definition of “money” is somewhat vague.

I believe there is a distinction to be made between a dollar note (money) vs capital. BTW: Dollar bills no longer exist, they're called "Federal Reserve Notes". Fractional Reserve Banking concept is key to understanding USD.

Banks make money by lending long and borrowing short.

It's kind of infuriating really to understand how it works. Banks have capital requirements which are extremely low. Good luck finding the documentation - I've searched. It's something less than like 6% or so. In other words, when you contractually obligate yourself to a 30 yr mortgage and borrow say 300,000USD for a home, the bank only has to have 18,000USD in it's account to cut your homebuilder a check for 300K which can immediately be cashed (money). The bank never had the money they lent you, yet they collect interest from you monthly on the whole $300k!

In short a "dollar" is a note. It represents debt - enforcer of work/behavior.